The invention relates to an air cooled condenser system that contains a steam-air heat exchanger (3) consisting of tubes (2) finned on the outside for the partial direct condensing of steam (1) with ambient air (4). This heat exchanger (3) receives the steam (1) from an upper distribution chamber (24) and ends in a lower chamber (25) which collects the condensate (8) and the steam (27) that has not yet condensed. The steam (22) not yet condensed in the steam-air heat exchanger (3) is condensed, in the steam-air section of the air cooled condenser, in a space operating as a direct contact condenser (9) by spraying water from the water-air cooling section (7) of the air cooled condenser, where the non-condensing gases are removed as well. The water (13) heated up in the direct contact condenser (9) is re-cooled in a water-air heat exchanger (7).